# Quadratic equations. The discriminant

If we have quadratic equation $ax^2+bx+c=0$, then the discriminant of the quadratic equation is the number D and it is found by formula: $$\displaystyle D=b^2-4ac$$ Then the solutions $(x_1 \ \text{and} \ x_2)$ of the quadratic equation we will find with this formula: $$\displaystyle x_{1,2}=\frac{-b \pm \sqrt{D}}{2a}$$ Number of solutions
If $D > 0$, then the quadratic equation thus has two distinct real solutions. If $D = 0$, then the quadratic equation has one real solution. If $D < 0$, then the quadratic equation has no real solutions.

Last time edited 2019-01-19

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